Teaching
Quantum Physics of Matter
A.P. E4100x (APPH 4100x)
3.0 points (lecture course)
Prerequisite: Physics 3021
Instructor: Professor Irving P. Herman
X4-4950, 905 Schapiro CEPSR, iph1@columbia.edu
Office hours: by appointment
Required text: "Introductory Quantum Mechanics," by R. Liboff, Addison-Wesley, 3rd Edition, 1998.
Course Description:
Basic theory of quantum mechanics, well and barrier problems, the
harmonic oscillator, angular momentum, identical particles, quantum
statistics, perturbation theory, and applications to the quantum
physics of atoms, molecules and solids.
Detailed Outline
1. Basic Postulates of Quantum Mechanics (Liboff Chapters 3 - 6)
a. Time independent and time dependent Schrodinger Equation
b. Dirac
notation, stationary states, Hilbert space, operators, commutators,
expectation values, different representations, momentum representation
(HW), Schrodinger vs. Heisenberg time evolution
2. One Dimensional Problems in Quantum Mechanics (Liboff Chapters 7 and 8)
a. Well and barrier problems (review)
i. Semiconductor layered structures (HW)
b. The harmonic oscillator - direct solution and operator approach
i. Diatomic molecule vibrations
A. Center of mass problems
B. Separable Hamiltonians
ii. SHO in many dimensions - Polyatomic molecule vibrations
iii. Lattice vibrations in a solid - acoustic and optical (HW) phonon modes
iv. Quantization of the electromagnetic field
v. Electron in a magnetic field - Landau levels (HW)
c. Elementary band theory of electrons in crystalline solids
i. Bonds vs. bands
ii. Free electron model - Brillouin zones
iii. Kronig-Penney model
iv. Solids - semiconductor bands, electrons and holes (heavy and light holes - HW), effective mass, quantum wells (also in HW)
v. Born Oppenheimer Approximation
d. WKB Approximation
3. Angular Momentum (Liboff Chapter 9)
a. General - operators
b. Orbital angular momentum - solutions, spherical harmonics
c. Addition of angular momentum - coupled and uncoupled representations
4. Three Dimensional Problems in Quantum Mechanics (Liboff Chapter 10)
a. Spherical symmetry, effective potentials
b. Free particles (also in HW)
c. Rotating Diatomic Molecule
i. Rigid rotor
ii. Uncoupled vibrational and rotational motion - perturbations (HW)
d. Hydrogen atom
i. Transitions, selection rules, matrix elements
5. More Theory in Quantum Mechanics (Liboff Chapters 11 and 13)
a. Matrix mechanics and changes of representation
b. Spin wavefunctions - Pauli spin matrices (HW)
c. Perturbation theory
i. Time independent - nondegenerate and degenerate
A. Stark effect in hydrogen atoms
B. Anharmonic corrections to SHO (HW) and rotor (HW)
C. Quantum-confined Stark effect (HW)
ii. Time dependent - and Fermi's golden rule
A. Absorption and stimulated emission
B. Transitions in an ideal two-level system (HW)
C. Spectroscopy, allowed transitions (also in HW)
6. Additional Applications of Quantum Mechanics in Matter (Liboff Chapter 12)
a. More exact treatment of one electron atoms - fine and hyperfine structure
b. Multi-electron atoms
i. Identical particles - wavefunctions for fermions and bosons
ii. Helium atoms - ground and excited states
A. Spectroscopic notation - electron configuration, term symbols
B. Electric dipole allowed transitions (also quadrupole in HW)
iii. Overview of Hartree (and Hartree-Fock) theory and results
iv. Atomic structure, x-rays (HW), Hund's rules, L-S coupling
v. Zeeman effect
c. Molecules and Molecular Structure
i. Ionic bonding
ii. Covalent bonding
A. H
2+ ion
B. H
2 molecule-molecular orbital and Heitler-London/valence bond methods
iii. Rotational, vibrational, and electronic transitions (Franck-Condon Principle)
iv. Consequences of identical nuclei in molecular states
7. Identical Particles and Quantum Statistics
a. Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann statistics
b. Free carriers in semiconductors
(HW - covered in homework)
Course grade determined by: 1 Midterm + 1 Final + several Homework Assignments.
